Without commenting on the dramatic appropriateness of Kirk's VoiceOver, Star Trek actually did it a couple of times that I can come up with off the top of my head. "Kirok" did it, and Spock did it when reflecting on Droxine, Vanna, and Stratos.
"These last few weeks, my love for Miramanee grows stronger with each passing day. However, the dreams return every night. Fragments of memories. I can almost get hold of them, and then...."
"This troubled planet is a place of the most violent contrasts. Those who receive the rewards are totally separated from those who shoulder the burdens. It is not a wise leadership. Here on Stratos, everything is incomparably beautiful and pleasant. The High Advisor's charming daughter Droxine, particularly so. The name Droxine seems appropriate for her. I wonder, can she retain such purity and sweetness of mind and be aware of the life of the people on the surface of the planet? There, the harsh life in the mines is instilling the people with a bitter hatred. The young girl who led the attack against us when we beamed down was filled with the violence of desperation. If the lovely Droxine knew of the young miner's misery, I wonder how the knowledge would affect her."